Subgroups — #18077926

Order 4864.

628 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926597	C₂	1	1	yes	maximal, characteristic
2	#14563703	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926270	C₂	1	2	yes	maximal
4	#14561478	C₂	1	2	yes	maximal
5	C₂×C₁₉×#387	C₂	1	1	yes	maximal, characteristic
6	#11926597	—	2	4	no	—
7	C₂×C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₂²⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄×C₁₉⋊C₈	—	2	1	no	—
11	#11926299	—	2	1	no	—
12	#11926299	—	2	1	no	—
13	#11926270	—	2	4	no	—
14	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#387	—	2	1	no	—
18	C₁₉×#387	—	2	1	no	—
19	C₁₉×#387	—	2	1	no	—
20	C₁₉×#387	—	2	1	no	—
21	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
22	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
23	C₂×C₁₉×#95	C₄	1	1	yes	characteristic
24	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
39	C₂×C₄⋊C₄×C₁₉	C₈	1	4	yes	complemented
40	C₂×C₄²×C₁₉	—	2	2	no	—
41	C₂×C₄²×C₁₉	—	2	2	no	—
42	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×C₁₉⋊C₈	—	2	2	no	—
47	C₂²×C₁₉⋊C₈	—	2	2	no	—
48	C₁₉×#95	—	2	1	no	—
49	C₁₉×#95	—	2	1	no	—
50	C₁₉×#95	—	2	1	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	C₁₉×#95	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉×#95	—	2	1	no	—
56	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₂²⋊(C₁₉⋊C₈)	D₄	1	4	yes	—
60	C₄⋊(C₁₉⋊C₈)	—	2	4	no	—
61	C₄×C₁₉⋊C₈	—	2	4	no	—
62	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	—	2	2	no	—
64	C₂²×C₄×C₁₉	—	2	2	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	2	no	—
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	4	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	4	1	no	—
80	C₂²×C₄×C₁₉	—	4	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	—	4	1	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	—	4	1	no	—
86	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
91	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
92	C₂²×C₄×C₁₉	C₂×C₈	1	2	yes	—
93	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
94	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	2	yes	—
98	C₄⋊C₄×C₁₉	—	2	4	no	—
99	C₄⋊C₄×C₁₉	—	2	4	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	2	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄²×C₁₉	—	2	1	no	—
104	C₄²×C₁₉	—	2	1	no	—
105	C₄²×C₁₉	—	2	2	no	—
106	C₄²×C₁₉	—	2	2	no	—
107	C₄²×C₁₉	—	2	1	no	—
108	C₄²×C₁₉	—	2	1	no	—
109	C₂×C₁₉⋊C₈	—	2	4	no	—
110	C₂×C₁₉⋊C₈	—	4	2	no	—
111	C₂×C₁₉⋊C₈	—	4	2	no	—
112	C₂×C₁₉⋊C₈	—	4	2	no	—
113	C₂×C₁₉⋊C₈	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	#9082	—	19	1	no	maximal, Sylow
116	C₂³×C₁₉	—	2	1	no	—
117	C₂³×C₁₉	—	2	1	no	—
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₉	C₄×D₄	1	2	yes	—
122	C₂³×C₁₉	C₂²×C₈	1	1	yes	characteristic
123	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
124	C₂³×C₁₉	#131	1	2	yes	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	4	no	—
136	C₂×C₄×C₁₉	—	2	4	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	2	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	4	2	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	4	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	—	4	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	8	2	no	—
160	C₂×C₄×C₁₉	—	8	2	no	—
161	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
162	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
163	C₂×C₄×C₁₉	#101	1	2	yes	—
164	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	2	yes	—
166	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
167	C₁₉⋊C₈	—	4	4	no	—
168	C₁₉⋊C₈	—	8	2	no	—
169	C₂×#431	—	19	1	no	—
170	C₂×#387	D₁₉	1	1	yes	characteristic
171	#1817	—	19	1	no	—
172	C₂×#324	—	19	2	no	—
173	#1280	—	19	2	no	—
174	C₂²×C₁₉	—	2	2	no	—
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	1	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	#386	1	1	yes	characteristic
183	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
184	C₂²×C₁₉	#408	1	1	yes	characteristic
185	C₂²×C₁₉	#410	1	1	yes	characteristic
186	C₂²×C₁₉	#410	1	1	yes	characteristic
187	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
188	C₂²×C₁₉	#413	1	1	yes	characteristic
189	C₂²×C₁₉	C₈×D₄	1	2	yes	—
190	C₂²×C₁₉	#435	1	2	yes	—
191	C₄×C₁₉	—	2	2	no	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	4	2	no	—
198	C₄×C₁₉	—	4	1	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	8	1	no	—
201	C₄×C₁₉	—	8	1	no	—
202	C₂²×C₄⋊C₄	Dic₁₉	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
204	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
205	#431	—	38	4	no	—
206	C₂×C₄⋊C₈	—	38	1	no	—
207	C₂×C₂²⋊C₈	—	19	2	no	—
208	C₂×C₂²⋊C₈	—	19	2	no	—
209	C₂×C₄×C₈	—	38	1	no	—
210	#387	—	2	1	no	—
211	#387	—	2	1	no	—
212	#387	—	2	1	no	—
213	#387	—	2	1	no	—
214	C₂×#95	Dic₁₉	1	1	yes	characteristic
215	C₂×#95	Dic₁₉	1	1	yes	characteristic
216	C₂×#95	Dic₁₉	1	1	yes	characteristic
217	C₂×#95	C₂×D₁₉	1	1	yes	characteristic
218	#336	—	38	1	no	—
219	#336	—	38	1	no	—
220	#324	—	38	4	no	—
221	C₂×C₁₉	—	2	2	no	—
222	C₂×C₁₉	—	2	2	no	—
223	C₂×C₁₉	#1458	1	1	yes	characteristic
224	C₂×C₁₉	#1461	1	1	yes	characteristic
225	C₂×C₁₉	#1470	1	1	yes	characteristic
226	C₂×C₁₉	#1473	1	1	yes	characteristic
227	C₂×C₁₉	#1869	1	1	yes	characteristic
228	C₂×C₁₉	#1899	1	1	yes	characteristic
229	C₂×C₁₉	#1901	1	1	yes	characteristic
230	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
231	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
232	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
233	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
234	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
235	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
236	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
237	C₂²×C₈	—	38	2	no	—
238	C₂²×C₈	—	38	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	C₁₉⋊C₈	1	4	yes	complemented
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	2	no	—
249	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
250	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
253	C₄⋊C₈	—	38	4	no	—
254	C₂²⋊C₈	—	19	4	no	—
255	C₂²⋊C₈	—	38	2	no	—
256	C₂²⋊C₈	—	38	2	no	—
257	C₂²⋊C₈	—	38	2	no	—
258	C₄×C₈	—	38	4	no	—
259	#95	—	2	1	no	—
260	#95	—	2	1	no	—
261	#95	—	2	1	no	—
262	#95	—	2	1	no	—
263	#95	—	2	1	no	—
264	#95	—	2	1	no	—
265	#95	—	2	1	no	—
266	#95	—	2	1	no	—
267	C₁₉	#9082	1	1	yes	characteristic, complemented, Sylow
268	C₂⁴	C₂²×Dic₁₉	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
293	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
294	C₂²×C₄	C₂×C₁₉⋊C₈	1	2	yes	—
295	C₂²×C₄	#64520	1	2	yes	—
296	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
297	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₁₉	1	2	yes	—
301	C₂²×C₄	#64543	1	2	yes	—
302	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
304	C₂×C₈	—	38	4	no	—
305	C₂×C₈	—	76	2	no	—
306	C₂×C₈	—	76	2	no	—
307	C₂×C₈	—	76	2	no	—
308	C₂×C₈	—	76	2	no	—
309	C₂×C₈	—	76	2	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	C₂²×C₁₉⋊C₈	1	1	yes	characteristic
326	C₂³	C₂×#64520	1	1	yes	characteristic
327	C₂³	D₄×Dic₁₉	1	2	yes	—
328	C₂³	#10597394	1	2	yes	—
329	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
367	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	2	yes	—
368	C₂×C₄	#10597293	1	2	yes	—
369	C₂×C₄	#10597381	1	1	yes	characteristic
370	C₂×C₄	#10597383	1	1	yes	characteristic
371	C₂×C₄	#10597385	1	2	yes	—
372	C₈	—	76	4	no	—
373	C₈	—	152	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	#11926424	1	1	yes	characteristic
383	C₂²	C₂×C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
384	C₂²	#11926511	1	1	yes	characteristic
385	C₂²	#11926518	1	1	yes	characteristic
386	C₂²	#11926518	1	1	yes	characteristic
387	C₂²	C₂×#10597293	1	1	yes	characteristic
388	C₂²	#11926528	1	1	yes	characteristic
389	C₂²	D₄×C₁₉⋊C₈	1	2	yes	—
390	C₂²	#11926616	1	2	yes	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	2	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	1	no	—
402	C₂	—	2	2	no	—
403	C₂	—	2	2	no	—
404	C₂	#14561949	1	1	yes	characteristic
405	C₂	#14561959	1	1	yes	characteristic
406	C₂	#14561991	1	1	yes	characteristic
407	C₂	#14562004	1	1	yes	characteristic
408	C₂	#14563928	1	1	yes	characteristic
409	C₂	#14564094	1	1	yes	characteristic
410	C₂	#14564104	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂³×C₁₉	C₂²×C₈
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#387	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²×C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#387	D₁₉
hypocenter	C₁₉	#9082
LCS	G ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#387

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
39. C₂×C₄⋊C₄×C₁₉	C₈	semidirect
246. C₂×C₄⋊C₄	C₁₉⋊C₈	semidirect
267. C₁₉	#9082	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11926597	2
#14563703	2
C₂×#11926270	2
#14561478	2
C₂×C₁₉×#387	2
#9082	19